All Questions ⁺⁰235714 Questions

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52

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+1439

circles

A circle is centered at $O.$ The tangent to the circle at $P$ is extended to $Q.$ Line segment $\overline{QS}$ intersects the circle at $R.$ Find the radius of the circle.

kittykat Dec 25, 2023

0

20

0

+1439

circles

Let $\overline{TU}$ and $\overline{VW}$ be chords of a circle, which intersect at $S$, as shown. Find $SW$.

kittykat Dec 25, 2023

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28

0

+1439

chords

Let $\overline{AB}$ and $\overline{CD}$ be chords of a circle, that meet at point $Q$ inside the circle. If $CD = 34$, then find the minimum length of $CQ$.

kittykat Dec 25, 2023

0

54

0

+1439

circles

Let $X$, $Y$, and $Z$ be points on a circle. Let line $XY$ and the tangent to the circle at $Z$ intersect at $W$. If $\overline{WY} \perp \overline{WZ}$, then find $YZ$.

kittykat Dec 25, 2023

0

41

1

+1439

chords

Chords $\overline{AB}$ and $\overline{CD}$ of a circle meet at $P$. If $AP = 3 \cdot PB$, then what is $AB$?

kittykat Dec 25, 2023

0

30

0

+1439

chords

Chords $\overline{PR}$ and $\overline{QS}$ of a circle are perpendicular. Find $RS$.

kittykat Dec 25, 2023

0

23

1

+1439

geometry

Let $\overline{XY}$ be a tangent to a circle, and let $\overline{XBA}$ be a secant of the circle, as shown below. If $AX = 10$ and $XY = 8$, then what is $AB$?

kittykat Dec 25, 2023

0

51

0

+1768

help with probability

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both have read more ..

bader Dec 25, 2023

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47

0

+1768

Counting

The following cards are split into three piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?

bader Dec 25, 2023

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16

1

+1768

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

bader Dec 25, 2023

0

25

1

+1768

Rolls

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $2000,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

bader Dec 25, 2023

Dec 24, 2023

0

16

1

+1439

Polygon

Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.
An equilateral triangle, a regular dodecagon, a square, and a regular $n$-gon, all with the same side length, also read more ..

kittykat Dec 24, 2023

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23

1

+1439

Polygon

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

kittykat Dec 24, 2023

0

29

1

+1439

Polygon

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

kittykat Dec 24, 2023

0

1

17

3

+27

Help plz. Thx

What is the smallest positive integer that is the sum of a multiple of $15$ and a multiple of $21$? (Remember that multiples can be negative.)

hellomeeee Dec 24, 2023

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16

1

+1439

Square

In the diagram, $ABCD$ is a square. Find $PR.$

M, N, O, L are midpoints of sides.
AB = 12 read more ..

kittykat Dec 24, 2023

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29

0

+1439

Polygons

Let $B,$ $A,$ and $D$ be three consecutive vertices of a regular $20$-gon. A regular heptagon is constructed on $\overline{AB},$ with a vertex $C$ next to $A.$ Find $\angle BAD,$ in degrees.

kittykat Dec 24, 2023

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31

0

+1439

Polygons

In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded hexagon.

kittykat Dec 24, 2023

0

34

1

+1678

Counting

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

wiseowl Dec 24, 2023

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26

1

+1678

Probability

Raina places the following balls into a bag. She draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 6 orange balls and 6 purple read more ..

wiseowl Dec 24, 2023

0

57

1

+1678

Counting

Joanna has seven beads that she wants to assemble into a bracelet. Five of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

wiseowl Dec 24, 2023

+1

10

6

+13

Sum and Product of Roots

Let the roots of the polynomial be . Evaluate
The answer is not 4.

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alibaba Dec 24, 2023

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56

0

+1911

Prism

A right rectangular prism has a total surface area of 2. Also, the sum of all the edges of the prism is 3. Find the length of the diagonal joining one corner of the prism to the opposite corner.

tomtom Dec 24, 2023

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37

0

+1911

Circle

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $2$ from one wall, and a distance of $2$ from the other wall. Find the radius read more ..

tomtom Dec 24, 2023

0

46

0

+1911

tangents

Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle TXU = 30^\circ$ and $\angle XTU = 90^\circ,$ then find $\angle QXR,$ in degrees.

tomtom Dec 24, 2023

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